Computing the implied volatility in stochastic volatility models

@article{Berestycki2004ComputingTI,
  title={Computing the implied volatility in stochastic volatility models},
  author={Henri Berestycki and J{\'e}r{\^o}me Busca and Igor Florent},
  journal={Communications on Pure and Applied Mathematics},
  year={2004},
  volume={57}
}
The Black-Scholes model [6, 23] has gained wide recognition on financial markets. One of its shortcomings, however, is that it is inconsistent with most observed option prices. Although the model can still be used very efficiently, it has been proposed to relax its assumptions, and, for instance, to consider that the volatility of the underlying asset S is no longer a constant but rather a stochastic process. There are two well-known approaches to achieve this goal. In the first class of models… 

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References

SHOWING 1-10 OF 25 REFERENCES

Pricing with a Smile

prices as a function of volatility. If an option price is given by the market we can invert this relationship to get the implied volatility. If the model were perfect, this implied value would be the

MANAGING SMILE RISK

Market smiles and skews are usually managed by using local volatility models a la Dupire. We discover that the dynamics of the market smile predicted by local vol models is opposite of observed

Implied and local volatilities under stochastic volatility

For asset prices that follow stochastic-volatility diffusions, we use asymptotic methods to investigate the behavior of the local volatilities and Black–Scholes volatilities implied by option prices,

STOCHASTIC IMPLIED TREES: ARBITRAGE PRICING WITH STOCHASTIC TERM AND STRIKE STRUCTURE OF VOLATILITY

In this paper we present an arbitrage pricing framework for valuing and hedging contingent equity index claims in the presence of a stochastic term and strike structure of volatility. Our approach to

Equivalent Black volatilities

We consider European calls and puts on an asset whose forward price F(t) obeys dF(t)=α(t)A(F)dW(t,) under the forward measure. By using singular perturbation techniques, we obtain explicit algebraic

Reconstruction of Volatility: Pricing Index Options by the Steepest Descent Approximation

We propose a formula for calculating the implied volatility of index options based on the volatility skews of the options on the underlying stocks and on a given correlation matrix for the basket.

Implied Trinomial Tress of the Volatility Smile

In options markets where there is a sign$cant or persistent volatility smile, implied tree models can ensure the consistency o f exotic options prices with the market prices o f liquid standard

Implied Trinomial Trees of the Volatility Smile

This material is for your private information, and we are not soliciting any action based upon it. This report is not to be construed as an offer to sell or the solicitation of an offer to buy any

Prices of State-Contingent Claims Implicit in Option Prices

This paper implements the time-state preference model in a multi-period economy, deriving the prices of primitive securities from the prices of call options on aggregate consumption. These prices